A242005 G.f. satisfies: 2*A(x) = 1 + x + A(x*A(x)^3).

1, 1, 3, 30, 478, 10146, 264303, 8084338, 282586248, 11085083577, 481673416483, 22956286840062, 1190639094701172, 66770638457654736, 4026673310312982723, 259904551978501682475, 17880944480665675868350, 1306415171298549344015316, 101032062583779191874828315

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..310

Formula

a(n) ~ c * 3^n * n^(n + 1/3*log(2)) / (exp(n) * (log(2))^n), where c = 0.33995993574240853...

Mathematica

nmax = 18; sol = {a[0] -> 1};
Do[A[x_] = Sum[a[k] x^k, {k, 0, n}] /. sol; eq = CoefficientList[2 A[x] - (1 + x + A[x A[x]^3]) + O[x]^(n + 1), x] == 0 /. sol; sol = sol ~Join~ Solve[eq][[1]], {n, 1, nmax}];
sol /. Rule -> Set;
a /@ Range[0, nmax] (* Jean-François Alcover, Nov 01 2019 *)

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A = 1+x + subst(A, x, x*A^3 +x*O(x^n)) - A); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A242003 (q=1), A242004 (q=2), A242006 (q=4).

Sequence in context: A360973 A359972 A218304 * A276356 A012003 A164945

Adjacent sequences: A242002 A242003 A242004 * A242006 A242007 A242008

Keyword

nonn

Author

Vaclav Kotesovec, Aug 11 2014

Extensions

Name corrected by Vaclav Kotesovec and Paul D. Hanna, Aug 15 2014

Status

approved